Regression Analysis: Towards Deep Learning

What is Regression Analysis?

Regression analysis is like finding a rule or formula that helps you predict something based on past data. It shows how two or more things (variables) are connected.

Real-Life Analogy

Imagine you want to know how much money you’ll earn if you sell lemonade:

• If you sell 1 glass, you earn ₹10.
• If you sell 2 glasses, you earn ₹20.
• If you sell 3 glasses, you earn ₹30.

You notice a pattern: Earnings = ₹10 × Number of glasses sold.

Here, you’re predicting earnings (output) based on the number of glasses sold (input). This is regression analysis!

Key Terms in Regression Analysis

1. Dependent Variable: What you want to predict. (Earnings ₹)
2. Independent Variable: The factor you use to predict. (Number of glasses sold)
3. Relationship: The formula that connects them. (Earnings = ₹10 × Glasses)

How Does Regression Work?

Regression analysis finds a line or curve that best fits the data points. This line (or equation) is used for prediction.

For example: If you sell 10 glasses, the line helps you predict earnings: Earnings = ₹10 × 10 = ₹100.

Types of Regression

1. Linear Regression: A straight-line relationship. Example: How earnings increase with the number of lemonade glasses sold.
2. Non-Linear Regression: A curved relationship. Example: How fast you run depends on how much energy you have (not a straight line).

Example: Predicting Exam Scores

Let’s say you want to predict how well students score based on how many hours they study.

Step 1: Collect Data

From 5 students:

• 1 hour → 20 marks
• 2 hours → 40 marks
• 3 hours → 60 marks
• 4 hours → 80 marks

Step 2: Find the Formula

The pattern is: Marks = 20 × Hours Studied

This is the regression equation: y = 20x where:

• y = Marks (dependent variable)
• x = Hours Studied (independent variable)

Step 3: Predict for New Data

If a student studies for 5 hours, the predicted marks are: y = 20 × 5 = 100 marks.

Why is Regression Useful?

1. Weather Forecasting: Predict tomorrow’s temperature based on past data.
2. House Pricing: Predict house prices based on location, size, and amenities.
3. Sports: Predict a player’s performance based on training hours.

How is Regression Related to Deep Learning?

Regression is like the foundation of machine learning and deep learning. Neural networks (used in deep learning) often perform tasks that are variations of regression, like predicting stock prices, recognizing objects in images, or even generating music.

Python Example: Predicting House Prices

Here’s a simple Python example for Linear Regression:

# Step 1: Import libraries
from sklearn.linear_model import LinearRegression
import numpy as np
# Step 2: Input data (size of house in square feet and price in ₹)
house_size = np.array([500, 1000, 1500, 2000]).reshape(-1, 1)
house_price = np.array([20, 40, 60, 80])  # Prices in ₹ Lakh
# Step 3: Train the model
model = LinearRegression()
model.fit(house_size, house_price)
# Step 4: Make a prediction
new_house_size = np.array([[2500]])  # Predict price for 2500 sqft house
predicted_price = model.predict(new_house_size)
# Step 5: Output the result
print(f"The predicted price for a 2500 sqft house is ₹{predicted_price[0]} Lakh.")

Output:

The predicted price for a 2500 sqft house is ₹100.0 Lakh.

Real-Life Connection: Regression in Action

Think about your exam results. A teacher might predict your score based on how much you study (hours) or your past performance (marks). Similarly, regression analysis helps find such patterns to make predictions for the future.

Summary

Regression analysis is about finding relationships and using them to make predictions. It’s a simple yet powerful tool used in weather forecasting, sports, business, and more. It’s also the building block of advanced AI systems!